Problem: Simplify the following expression: $\dfrac{60p^4}{42p^2}$ You can assume $p \neq 0$.
Explanation: $ \dfrac{60p^4}{42p^2} = \dfrac{60}{42} \cdot \dfrac{p^4}{p^2} $ To simplify $\frac{60}{42}$ , find the greatest common factor (GCD) of $60$ and $42$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $42 = 2 \cdot 3 \cdot 7$ $ \mbox{GCD}(60, 42) = 2 \cdot 3 = 6 $ $ \dfrac{60}{42} \cdot \dfrac{p^4}{p^2} = \dfrac{6 \cdot 10}{6 \cdot 7} \cdot \dfrac{p^4}{p^2} $ $\phantom{ \dfrac{60}{42} \cdot \dfrac{4}{2}} = \dfrac{10}{7} \cdot \dfrac{p^4}{p^2} $ $ \dfrac{p^4}{p^2} = \dfrac{p \cdot p \cdot p \cdot p}{p \cdot p} = p^2 $ $ \dfrac{10}{7} \cdot p^2 = \dfrac{10p^2}{7} $